Page 126 - MEMS Mechanical Sensors

6.2 Physics of Pressure Sensing 115

h P d
A
t

P b

Figure 6.3 Pressures on a submerged block.

by the downwards pressure on the top face of the block, p [given by (6.1)], minus
d
this buoyancy pressure, is given by

p = (h t+ ) gρ (6.2)
b
p − p = ρ (6.3)
t g
d b
This is the basic principle by which objects float in liquids. If the weight of a
displaced liquid exceeds the weight of the object, then it has positive buoyancy and
will float on the surface. Conversely, if the weight of the object exceeds the weight
of the liquid it will have negative buoyancy and sink. Neutral buoyancy is obtained
by when the weight of the object equals the weight of displaced liquid, and there-
fore P = P . Objects with neutral buoyancy will remain suspended in the liquid at
b d
whatever depth they are located. Submarines, for example, typically operate at
neutral buoyancy and change depth by angling fins and moving forward.
Atmospheric pressure is related to the above case. The fluid in question is the
Earth’s atmosphere, which extends to a height of 150 km. The calculation of atmos-
pheric pressure is complicated by the fact that the density of the atmosphere varies
with height due to the Earth’s gravitational field and the compressible nature of
gases. Liquids, on the other hand, are nearly incompressible and therefore this com-
plication does not occur. The atmospheric pressure at the Earth’s surface is referred
to as 1 atmosphere (numerous equivalent units of pressure were given in Table 6.1).
The incompressible nature of liquids enables them to be used in hydraulic sys-
tems. Pascal’s principle states that a liquid can transmit an external pressure applied
in one location to other locations within an enclosed system. By applying the pres-
surizing force on a small piston and connecting this to a large piston, mechanical
amplification of the applied force can be achieved, as shown in Figure 6.4. The dis-
tance moved by the larger piston will be less than that moved by the smaller piston,
as shown in (6.4). This principle is used in hydraulic car jacks and presses.

F A
d = 1 d = 1 d (6.4)
2
F 1 A 1
2 2
The rules applying to static pressures described above no longer apply when
pressure measurement is carried out in moving fluids. Bernoulli’s investigations of
the forces present in a moving fluid identified two components of the total pressure
of the flow: static and dynamic pressure. Bernoulli’s equation, one form of which is